where \(G\)  is the Gibbs free energy per unit area of the cell, \(A\)  is the cell's area, \(\dot{Q}_\mathrm {irr}\)  is the energy dissipated per unit area and \(I\)  and \(V\)  are the current drawn by and the potential drop across the cell. The physical interpretation of this law is that the left-hand side of (REF ) represents the rate of change of the total chemical energy within the cell, while the terms on the right-hand side represent the rate of energy drawn from the cell. In particular, the terms on the right-hand side can be sub-divided into \(I V\) , the useful electrical power produced by the device, and \(A \dot{Q}_\mathrm {irr}\) , the rate of irreversible energy dissipation (to heat). Further details, on the computation of \(G\)  and \(\dot{Q}_\mathrm {irr}\)  from the solution of the DFN model, together with a mathematical proof of this result and its numerical validation, can be found in [1]}. This formulation provides all the contributions to the irreversible heat generation, which need to be considered in coupled thermal-electrochemical models of a battery. A similar consistent theory has been proposed for the microscopic model by Latz & Zausch [2]}, [3]}.
